Melt the 1 tablespoon margarine or butter in a large saucepan. Add onion. Cover and cook over medium-low heat about 15 minutes or until onion is tender and golden, stirring occasionally. Sprinkle sugar over onion. Cook, covered, for 10 to 15 minutes more or until browned, stirring occasionally. Stir in hazelnuts or walnuts. Cool.
Work with one sheet of phyllo at a time, keeping remaining sheets covered with plastic wrap until needed. Lightly brush one sheet of phyllo dough with some of the 1/4 cup melted margarine or butter. Place another sheet of phyllo dough on top of the first sheet, and brush with margarine or butter. Repeat with two more sheets of phyllo, brushing with margarine or butter. Cut a 12-inch circle from the stack; discard trimmings.
Slice one round of Brie or camembert in half horizontally. Place bottom half in center of phyllo stack. Spread with 1 tablespoon of the apricot spreadable fruit; top with one-fourth of the caramelized onion-hazelnut mixture. Top with other half of Brie, 1 tablespoon spreadable fruit, and another one-fourth of onion-hazelnut mixture. Wrap phyllo up and over filling, pleating phyllo as needed to cover and slightly twisting phyllo on top. Brush phyllo with margarine or butter. Repeat with remaining phyllo, margarine, Brie, spreadable fruit, and onion-hazelnut mixture.
Place one wrapped Brie round in an 8x8x2-inch baking pan or two rounds in a 13x9x2-inch baking pan. Cover and chill up to 24 hours. Bake in a 400 degree F oven about 20 minutes or until golden. Let stand 5 to 10 minutes. Serve with bread, fruit wedges, or crackers. Makes 12 servings.